NUMBER

Divisibility Rules

Learn the reliable method for divisibility rules, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

Divisibility rules test whether a number divides exactly without a remainder.

Picture itFollow the number relationship
2 · THE METHOD

Follow these steps

  1. Choose the rule for each required divisor.
  2. Test every condition against the whole number.
  3. Confirm that all required rules hold, not just one.
3 · WORKED EXAMPLES

See the method in action

Example 1

Which number is divisible by 5?

  1. A whole number is divisible by 5 when its last digit is 0 or 5.
  2. Only 135 meets this rule.
Answer: 135
Example 2

The candidates are 504, 510, 508, 506, 505. Identify the one number divisible by both 3 and 4, then divide it by 12. What is the quotient?

  1. The digit sum of 504 is 9, a multiple of 3, and its final two digits, 04, form a multiple of 4.
  2. The other candidates fail at least one test.
  3. Finally, 504 ÷ 12 = 42.
Answer: 42
4 · ELEVENSPRINT TIP

A useful shortcut

Confirm that all required rules hold, not just one.

5 · COMMON MISTAKES

Watch out for these

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.